Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: MS = MatrixSpace(ZZ,4,6)
sage: u = MS.dimension()
sage: u - 24 == 0
True
dims()
Returns (m row, n col) representation of self dimension
EXAMPLES:
sage: MS = MatrixSpace(ZZ,4,6)
sage: MS.dims()
(4, 6)
full_category_initialisation()
Make full use of the category framework.
NOTE:
It turns out that it causes a massive speed regression in computations with elliptic curves, if a full initialisation
of the category framework of matrix spaces happens at initialisation: The elliptic curves code
treats matrix spaces as containers, not as objects of a category. Therefore, making full use of the category
framework is now provided by a separate method (see trac ticket #11900).
EXAMPLES:
sage: MS = MatrixSpace(QQ,8)
sage: TestSuite(MS).run()
Failure in _test_category:
Traceback (most recent call last):
...
AssertionError: category of self improperly initialized
------------------------------------------------------------
The following tests failed: _test_category
sage: type(MS)
sage: MS.full_category_initialisation()
sage: TestSuite(MS).run()
sage: type(MS)
Todo
Add instead an optional argument to MatrixSpace() to temporarily disable the category initialization
in those special cases where speed is critical:
sage: MS = MatrixSpace(QQ,7, init_category=False) # todo: not implemented
sage: TestSuite(MS).run()
# todo: not implemented
Traceback (most recent call last):
...
AssertionError: category of self improperly initialized
until someone recreates explicitly the same matrix space without that optional argument:
sage: MS = MatrixSpace(QQ,7)
sage: TestSuite(MS).run()
# todo: not implemented
# todo: not implemented
gen(n)
Return the n-th generator of this matrix space.
6 Chapter 1. Matrix Spaces